Modelling and visualization of signals (including time-series and other forms of data sequences) have application in many fields, including mechanics, electronics, medicine, and audio processing for entertainment or intelligence.
The process of modelling a signal generally involves generating a mathematical representation of the signal referred to as a signal model, which can be used to generate a signal which may be identical to the signal being modelled, or more typically provides a close approximation to it. Existing signal models generally emphasize a certain aspect of the signal, as described further below. Depending on the task and field of application, a model is chosen accordingly to obtain a representation of a signal with emphasis on the corresponding aspect. The model is then used to generate a model signal or model instance representing the original signal, and this generated signal is either used directly or is visualized in some way.
One common signal model or representation, referred to as a ‘waveform’, represents the signal as an ordered sequence of amplitude values and associated respective values of time (or other variable on which the amplitudes depend), and is used when reproducing the signal or storing it as ‘raw data’. A visualization of a waveform model is displayed directly as a graph of the signal amplitudes against the time values (or other variable values, as appropriate). Such visualizations can be readily comprehended by non-expert users, but are not compact, and may require inefficient zooming and scrolling to view particular portions of the signal.
Models based on Fourier or wavelet transforms represent the signal as a set of rather abstract coefficients that highlight the spectral or scalar aspects of the signal. Visualizations of such models display these coefficients as colour-coded values in a one or two dimensional domain. Such visualizations are more compact than waveform visualizations, but require a considerable amount of experience to interpret, and are not readily comprehended by non-expert users. Moreover, such models often involve applying ‘windows’ or otherwise filtering the signal, which limits the level of detail and accuracy of the model.
One signal aspect which is not well represented in any of the available models is referred to herein as the ‘waveshape’, i.e., the general geometric shape or morphology of a waveform, considered for the length of a signal cycle or period (assuming a periodic or quasi-periodic signal). The waveshape and its evolution over time can be an important aspect of a signal, e.g., when representing heart or other physiological conditions, faults in rotating or reciprocating machinery, or the timbre of a voice, musical instrument or other audio signal. Common examples of basic waveshapes include the ‘square’, ‘sine’ or ‘triangle’ waveshapes. Viewed qualitatively, a waveshape does not depend on the length of the corresponding signal cycle or period measured in time. For example, the waveshapes of a sine wave at a frequency of 50 Hz and a sine wave at 100 Hz are identical. It would be useful to provide a representation or visualization which describes the state and the evolution of the waveshape in a manner that is readily comprehended by non-expert users.
It is desired to provide a signal process and system and a normalisation process and system that alleviate one or more of the above difficulties, or at least that provide a useful alternative.